Intensity Of Jumps Research Articles

On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations.

The fundamental solution of the master equation for a jump‐diffusion Ornstein–Uhlenbeck process

AbstractAn integro‐differential equation for the probability density of the generalized stochastic Ornstein–Uhlenbeck process with jump diffusion is considered for a special case of the Laplacian distribution of jumps. It is shown that for a certain ratio between the intensity of jumps and the speed of reversion, the fundamental solution can be found explicitly, as a finite sum. Alternatively, the fundamental solution can be represented as converging power series. The properties of this solution are investigated. The fundamental solution makes it possible to obtain explicit formulas for the density at each instant of time, which is important, for example, for testing numerical methods.

Time-varying jump intensity and volatility forecasting of crude oil returns

Modelling and forecasting of crude oil volatility have been widely examined using GARCH-type models, and evidence suggests the presence of time-varying jumps in the crude oil market. This paper proposes a novel approach to model and forecast crude oil volatility by incorporating two time-varying jump intensities (State-dependent and Hawkes process) into the GARCH-Jump model. Our in-sample and out-of-sample analysis demonstrates that considering jump intensity as an explanatory variable significantly enhances the forecasting accuracy of WTI and Brent crude oil volatility. For WTI crude oil volatility, the more complex the jump intensity model, the better its forecasting power. For Brent crude oil volatility, the picture is different, indicating that the non-linear characteristics of volatility provide more informative forecasts. Further analysis shows that, during the COVID-19 crisis period, the Hawkes Jump Intensity (HJI)-GARCH model consistently improves the volatility forecasting performance. These results highlight the importance of jump intensity in modelling and predicting crude oil price volatility.

Asymptotic Normality of Bias Reduction Estimation for Jump Intensity Function in Financial Markets

Continuous‐time diffusion models with jumps, especially the jump intensity coefficient, can depict the impact of sudden and large shocks to financial markets. It is possible to disentangle, from the discrete observations, the contributions given by the jumps and those by the diffusion part through threshold functions. Based on this threshold technique, we employ non‐parametric local linear threshold estimator for the unknown jump intensity function of a semimartingale with jumps. The asymptotic normality of our estimator is provided in the presence of finite activity jumps under certain regular conditions. The finite‐sample performance for the underlying estimator has been shown through a Monte Carlo experiment and an empirical analysis on high frequency returns of indexes in the USA and China.

An $$L_q(L_p)$$-theory for space-time non-local equations generated by Lévy processes with low intensity of small jumps

An $$L_q(L_p)$$-theory for space-time non-local equations generated by Lévy processes with low intensity of small jumps

Методика раціонального формування поверхонь гальмування плоского надзвукового вхідного пристрою

This article deals with methodological support for the design of effective supersonic flat external compression input devices. A concise analysis of the contribution of well-known scientists in the study of braking processes of supersonic flows of the working body in the system of sealing jumps is presented in the input devices. The proposed method of rational formation of the braking surfaces of a flat supersonic inlet device is based on the main provisions of the gas-hydraulic theory of sealing jump proposed by Rankin and Hugoniot. The main goal of this study is the development of a method of rational formation of braking surfaces of a supersonic flat input device of external compression according to the criterion of its efficiency, namely the maximum value of the coefficient of preservation of full pressure in sealing jumps. The choice of the value of the angle of inclination of the braking surfaces of the supersonic input device and the corresponding angles of inclination of the oblique jumps of the seal for a given calculated value of the number M consists in finding such values of the angles of inclination of the braking surfaces, at which the intensity of the oblique jumps of the seal is the same, under this condition the coefficient of preservation of full pressure is maximum. The mathematical formulation of the problem of determining the rational position of the braking surfaces of the supersonic flat input device of external compression is possible in the form of finding the angle of inclination of the first braking surface, which corresponds to the maximum value of the coefficient of preservation of full pressure for the determined value of the number M before the first oblique jump of the seal and at a constant intensity of the oblique jumps of the seal. This article outlines the main elements of the proposed methodology. Using the given methodology, a rational value of the angle of inclination of the first oblique jump of the seal was searched for the calculated value of the number M=2.5. In the supersonic input device operating at the specified design number M, three oblique sealing jumps and one direct-closing sealing jump are selected. The dependence of the full pressure preservation coefficient of oblique sealing jumps, direct jump, and total pressure preservation coefficient in the sealing jumps of the supersonic inlet device is obtained. It is shown that with an increase in the angle of inclination of the first braking surface and the corresponding values of the angles of inclination of the second and third braking surfaces, the coefficient of preservation of the full pressure of oblique jumps of the seal decreases, and that of direct jumps increases, which determines the presence of an extremum and makes it possible to determine the rational value of the angle of inclination of the first braking surface. This technique allows for any number of M before the first oblique jump of the seal to determine the rational values of the angles of inclination of the braking surfaces of the flat supersonic external compression input device.

Methodological considerations for determining the volume and intensity of drop jump training. A systematic, critical and prepositive review.

passive or active control group during a plyometric training program. information on improvement with Drop Jump or Depth Jump, with other jumps, acceleration, sprint, strength, and power output. randomized controlled trials. We searched articles published in PubMed, SPORTDiscus, Web of Science, and Scopus. The search was conducted until 10 September 2022 for English-language articles only. The risk of bias was assessed using Grading of Recommendations, Assessment, Development and Evaluation (GRADE) for randomized controlled studies. We identified 31495 studies, of which only 22 were included. We found that six groups presented results with women, 15 presented results with men, and the remaining four presented mixed studies. Of the 686 people recruited, 329 participants aged 25.79 ± 4.76years were involved in training. Methodological problems in training intensity, volume distribution, and individualization were noted, but methodological recommendations for their solution are also provided. It is concluded that the drop height should not be understood as the intensity determinant of plyometric training. Intensity is determined by ground reaction forces, power output, and jump height, among other factors. Furthermore, the athletes' experience level selection should be based on the formulas recommended within this research. These results could be helpful for those who intend to conduct new plyometric training programs and research.

Short Communication: A Primer on Perpetuals

We consider a continuous-time financial market with no arbitrage and no transactions costs. In this setting, we introduce two types of perpetual contracts, one in which the payoff to the long side is a fixed function of the underlyers and the long side pays a funding rate to the short side, the other in which the payoff to the long side is a fixed function of the underlyers times a discount factor that changes over time but no funding payments are required. Assuming asset prices are continuous and strictly positive, we derive model-free expressions for the funding rate and discount rate of these perpetual contracts as well as replication strategies for the short side. When asset prices can jump, we derive expressions for the funding and discount rates, which are semirobust in the sense that they do not depend on the dynamics of the volatility process of the underlying risky assets, but do depend on the intensity of jumps under the market’s pricing measure. When asset prices can jump and the volatility process is independent of the underlying risky assets, we derive an explicit replication strategy for the short side of a perpetual contract. Throughout the paper, we illustrate through examples how specific perpetual contracts relate to traditional financial instruments such as variance swaps and leveraged exchange traded funds.

Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems

We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the Hölder exponent of the Hessian of the limit problem, and explain how correction terms can be constructed. This provides an alternative efficient method for the numerical approximation of the optimal control of a pure-jump problem in situations with very high intensity of jumps. We illustrate this approach in the context of a display advertising auction problem.

In search of time-varying jumps during the turmoil periods: Evidence from crude oil futures markets

Prior literature demonstrates that energy prices are characterized by time-varying jumps. However, earlier studies do not investigate if the intensity of such jumps appears to be higher amid periods of extreme volatility in comparison to normal periods. Employing the GARCH-jump model, this study examines whether jumps occurring in energy prices are an indicator of market crashes. To serve this purpose, we consider several downturns in oil markets spanning over the last few years. Our empirical analyses reveal that the conditional expected number of jumps in WTI and Brent oil futures prices increases significantly amid the depression periods, which is, however, not the case when the market functions normally. We, therefore, conclude that such clusters of jumps may contain predictive information for oil market crashes and thus provide early signals of future downturns. The findings further show that crude oil volatility, the US equity VIX, and economic policy uncertainty play a significant role in explaining the time-dependent jumps during the turmoil periods. The findings of our research could be useful for investors participating in global crude oil markets and for policymakers watching out for the impact of energy prices on the economy.

News Arrival, Time-Varying Jump Intensity, and Realized Volatility: Conditional Testing Approach

Abstract This paper introduces new econometric tests to identify stochastic intensity jumps in high-frequency data. Our approach exploits the behavior of a time-varying stochastic intensity and allows us to assess how intensely stock market reacts to news. We describe the asymptotic properties of our test statistics, derive the associated central limit theorem and show in simulations that the tests have good size and reasonable power in finite-sample cases. Implementing our testing procedures on the S&P 500 exchange-traded fund data, we find strong evidence for the presence of intensity jumps surrounding the scheduled Federal Open Market Committee (FOMC) policy announcements. Intensity jumps occur very frequently, trigger sharp increases in realized volatility and arrive when differences in opinion among market participants are large at times of FOMC press releases. Unlike intensity jumps, volatility jumps fail to explain the variation in news-induced realized volatility.

Conditional Probability of Jumps in Oil Prices

The objective of this research is to model the behavior of oil returns. The volatility of oil returns is described through a TGARCH process. Conditional probability jumps are incorporated through uniform, double exponential and normal jump intensity distributions. We found that the volatility of oil returns follows the stylized facts of leptokurtosis, leverage effect and volatility clustering. The abnormal information that causes the jumps, can cause another type of unexpected changes in the following period and the intensity of the jumps has a negative effect on the probability of jumps in the next period. The dynamic model proposed can be extended to other markets and to multivariate time series modeling considering the dependence among the markets’ returns. The main contribution of this work is the estimation of the conditional probability of jumps depending on the previous behavior leading to a better description of the stochastic dynamics of crude oil prices. This will be useful for making better decisions regarding oil as an underlying asset in derivatives or in the formulation of better public policies.

Global Position Analysis during Official Elite Female Beach Volleyball Competition: A Pilot Study

The aim of this study was to quantify the physical demands of female beach volleyball competition with reference to player position, set, and match outcome. Twelve professional players were equipped with a 10 Hz GPS device (Minimax S4, Catapult Sports, Australia). Data collection occurred over 30 official matches, with a total of 50 sets. GPS output variables were related to position (e.g., Defenders and Blockers). Differences between players’ positions were found in Peak Player Load, the distance covered at different intensities, and acceleration and deceleration. Variations during the match were more pronounced for Defenders than for Blockers, with the former increasing the intensity of acceleration and deceleration, and decreasing the velocity of displacements and lower jumps. For Blockers, main variations occurred between the first and second set, with a reduction in velocity displacements and an increase in the intensity of jumps. Defender variables that contributed to victory were high deceleration, velocity, acceleration, and Peak Player Load. The characteristics of Blockers that contributed to victory were maximum velocity and high jumps. Female beach volleyball players seem to have different physiological requirements according to their position. The analysis of these variations throughout the game suggests that a specific player’s position output may be determined by proper and/or opponent tactical schemes.

The Law of the Iterated Logarithm for Random Dynamical System with Jumps and State-Dependent Jump Intensity

Abstract In this paper our considerations are focused on some Markov chain associated with certain piecewise-deterministic Markov process with a statedependent jump intensity for which the exponential ergodicity was obtained in [4]. Using the results from [3] we show that the law of iterated logarithm holds for such a model.

Hawkes-based models for high frequency financial data

Compared with low frequency data, high frequency data exhibit distinct empirical properties, including, for instance, essentially discontinuous evolution paths, time-varying intensities, and self-exciting features. All these make it more challenging to model appropriately the dynamics associated with high frequency data such as order arrival and price formation. To capture more accurately the microscopic structures and properties pertaining to the limit order books, this paper focuses on modeling high frequency data using Hawkes processes. Two models, one with exponential kernels and the other with power-law kernels, are introduced systematically, algorithmized precisely, and compared with each other extensively from various perspectives, including the goodness of fit to the original data and the computational time in searching for the maximum likelihood estimator, with search algorithm being taken into consideration as well. To measure the goodness of fit, a number of quantities are proposed. Studies based on both multiple-trading-day data of one stock and multiple-stock data on one trading day indicate that Hawkes processes with slowly-decaying kernels are able to reproduce the intensity of jumps in the price processes more accurately. The results suggest that Hawkes processes with power-law kernels and their implied long memory nature of self-excitation phenomena could, on the level of microstructure, serve as a realistic model for high frequency data.

Pricing vulnerable options with jump risk and liquidity risk

In this paper, we consider vulnerable options with jump risk and liquidity risk. In the proposed framework, we allow discontinuous changes in the information processes and the liquidity discount factors as well, and default risk is taken into consideration. Specially, we investigate the effect of jumps in the liquidity discount factors and find that the effects of jumps in the liquidity discount factors are stable for different maturities and alternative moneynesses. Further, option prices behave differently with respect to alternative intensities of common jumps, depending on whether there are jumps in the liquidity discount factors or not.

Estimates of Dirichlet heat kernels for unimodal Lévy processes with low intensity of small jumps

In this paper, we study transition density functions for pure jump unimodal L\'evy processes killed upon leaving an open set $D$. Under some mild assumptions on the L\'evy density, we establish two-sided Dirichlet heat kernel estimates when the open set $D$ is $C^{1, 1}$. Our result covers the case that the L\'evy densities of unimodal L\'evy processes are regularly varying functions whose indices are equal to the Euclidean dimension. This is the first results on two-sided Dirichlet heat kernel estimates for L\'evy processes such that the weak lower scaling index of the L\'evy densities is not necessarily strictly bigger than the Euclidean dimension.

Neuromuscular Adaptations and Enhancement of Physical Performance in Female Basketball Players After 8 Weeks of Plyometric Training.

The aim of this study was to examine the effects of an 8-week in-season plyometric training (PT) program on the physical performance and neuromuscular adaptations of female basketball players. Twenty-seven elite female basketball players (aged 21.0 ± 2.6 years) were assigned between an experimental group (n = 15) who substituted a part of their usual training with biweekly PT, and a control group (n = 12) who maintained their standard basketball training. Analyses of variance and co-variance assessed changes in 10, 20, and 30 m sprint times, ability to change direction (T-test) and jumping ability [squat jump (SJ) and countermovement jump (CMJ)] with electromyographic assessment of the vastus lateralis, vastus medialis, and rectus femoris muscles during jumping and meassurement of the isokinetic strength of the knee muscles. After 8 weeks of the plyometric program the experimental group enhanced change of direction performance (Δ = −3.90%, d = 0.67) and showed a greater thigh cross sectional area (Δ = 9.89%, d = 0.95) relative to controls. Neural adaptations included significant improvements of EMG parameters for the vastus medialis muscle during Squat Jumping (Δ = 109.3%, d = 0.59). However, trends to improvements of sprinting times and jumping performances did not reach statistical significance. In addition, there were no gains in the peak torque and the average power of the quadriceps and hamstring muscles at either slow or moderate test speeds. We conclude that 8-weeks of PT (72–126 jumps) was insufficient to improve many of the variables associated with basketball performance in our subject-group. Further studies of female basketball players, extending the program period and increasing the intensity and speed of jumps are recommended in the search for more significant results.

Forecasting China's Crude Oil Futures Volatility: The Role of the Jump, Jumps Intensity, and Leverage Effect

AbstractThis study explores the forecasting ability of jump, jump intensity, and leverage effect for an emerging futures market, China's crude oil futures market, using different kinds of HAR‐type models. From an in‐sample perspective, we find that the HAR components, monthly leverage effect, jump size, and jump intensity have positive effects on future oil volatility. Moreover, out‐of‐sample results show that a forecasting model with jump and jump intensity cannot only achieve a superior forecasting performance under low volatility level but also increase the economic value. Subsequently, we examine the effect of decompositions of jump information, the results show signed jump components can improve the accuracy. Finally, we extend our empirical analysis considering different forecast horizons, COVID‐19 pandemic, and different trading hours. Our empirical results are robust and consistent.

The Impact of Forecasting Jumps on Forecasting Electricity Prices

The paper is devoted to forecasting hourly day-ahead electricity prices from the perspective of the existence of jumps. We compare the results of different jump detection techniques and identify common features of electricity price jumps. We apply the jump-diffusion model with a double exponential distribution of jump sizes and explanatory variables. In order to improve the accuracy of electricity price forecasts, we take into account the time-varying intensity of price jump occurrences. We forecast moments of jump occurrences depending on several factors, including seasonality and weather conditions, by means of the generalised ordered logit model. The study is conducted on the basis of data from the Nord Pool power market. The empirical results indicate that the model with the time-varying intensity of jumps and a mechanism of jump prediction is useful in forecasting electricity prices for peak hours, i.e., including the probabilities of downward, no or upward jump occurrences into the model improves the forecasts of electricity prices.